Question

A toroidal core with 3000 turns has inner and outer radii of 11 cm and 12 cm, respectively. When a current of 0.70 A is passed, the magnetic field produced in the core is 2.5 T. Find the relative permeability of the core. (μ₀ = 4π x 10⁻⁷ T m A⁻¹)

Answer 1

magnetic field due to a torroid is given by

$B = \frac{\mu_r \mu_0 N i}{2\pi R}$

here R = mean radius

$R = \frac{R_{in} + R_{out}}{2}$

$R = \frac{11 + 12}{2} = 11.5 cm$

now by above formula

N = 3000

i = 0.70 A

B = 2.5 T

now by plug in all values

$2.5 = \frac{\mu_r * 4\pi * 10^{-7}* 3000 * 0.70}{2 \pi * 0.115}$

$\mu_r = 684.5$

so the relative permeability will be 684.5